Polytope of Type {42,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {42,14}*1176b
Also Known As : {42,14|2}. if this polytope has another name.
Group : SmallGroup(1176,265)
Rank : 3
Schlafli Type : {42,14}
Number of vertices, edges, etc : 42, 294, 14
Order of s0s1s2 : 42
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {14,14}*392a
7-fold quotients : {6,14}*168, {42,2}*168
14-fold quotients : {21,2}*84
21-fold quotients : {2,14}*56, {14,2}*56
42-fold quotients : {2,7}*28, {7,2}*28
49-fold quotients : {6,2}*24
98-fold quotients : {3,2}*12
147-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 8, 43)( 9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 36)
( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)( 23, 30)
( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 50, 99)( 51,100)( 52,101)
( 53,102)( 54,103)( 55,104)( 56,105)( 57,141)( 58,142)( 59,143)( 60,144)
( 61,145)( 62,146)( 63,147)( 64,134)( 65,135)( 66,136)( 67,137)( 68,138)
( 69,139)( 70,140)( 71,127)( 72,128)( 73,129)( 74,130)( 75,131)( 76,132)
( 77,133)( 78,120)( 79,121)( 80,122)( 81,123)( 82,124)( 83,125)( 84,126)
( 85,113)( 86,114)( 87,115)( 88,116)( 89,117)( 90,118)( 91,119)( 92,106)
( 93,107)( 94,108)( 95,109)( 96,110)( 97,111)( 98,112)(155,190)(156,191)
(157,192)(158,193)(159,194)(160,195)(161,196)(162,183)(163,184)(164,185)
(165,186)(166,187)(167,188)(168,189)(169,176)(170,177)(171,178)(172,179)
(173,180)(174,181)(175,182)(197,246)(198,247)(199,248)(200,249)(201,250)
(202,251)(203,252)(204,288)(205,289)(206,290)(207,291)(208,292)(209,293)
(210,294)(211,281)(212,282)(213,283)(214,284)(215,285)(216,286)(217,287)
(218,274)(219,275)(220,276)(221,277)(222,278)(223,279)(224,280)(225,267)
(226,268)(227,269)(228,270)(229,271)(230,272)(231,273)(232,260)(233,261)
(234,262)(235,263)(236,264)(237,265)(238,266)(239,253)(240,254)(241,255)
(242,256)(243,257)(244,258)(245,259);;
s1 := ( 1, 57)( 2, 63)( 3, 62)( 4, 61)( 5, 60)( 6, 59)( 7, 58)( 8, 50)
( 9, 56)( 10, 55)( 11, 54)( 12, 53)( 13, 52)( 14, 51)( 15, 92)( 16, 98)
( 17, 97)( 18, 96)( 19, 95)( 20, 94)( 21, 93)( 22, 85)( 23, 91)( 24, 90)
( 25, 89)( 26, 88)( 27, 87)( 28, 86)( 29, 78)( 30, 84)( 31, 83)( 32, 82)
( 33, 81)( 34, 80)( 35, 79)( 36, 71)( 37, 77)( 38, 76)( 39, 75)( 40, 74)
( 41, 73)( 42, 72)( 43, 64)( 44, 70)( 45, 69)( 46, 68)( 47, 67)( 48, 66)
( 49, 65)( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)
(113,141)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,134)
(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(128,133)(129,132)
(130,131)(148,204)(149,210)(150,209)(151,208)(152,207)(153,206)(154,205)
(155,197)(156,203)(157,202)(158,201)(159,200)(160,199)(161,198)(162,239)
(163,245)(164,244)(165,243)(166,242)(167,241)(168,240)(169,232)(170,238)
(171,237)(172,236)(173,235)(174,234)(175,233)(176,225)(177,231)(178,230)
(179,229)(180,228)(181,227)(182,226)(183,218)(184,224)(185,223)(186,222)
(187,221)(188,220)(189,219)(190,211)(191,217)(192,216)(193,215)(194,214)
(195,213)(196,212)(246,253)(247,259)(248,258)(249,257)(250,256)(251,255)
(252,254)(260,288)(261,294)(262,293)(263,292)(264,291)(265,290)(266,289)
(267,281)(268,287)(269,286)(270,285)(271,284)(272,283)(273,282)(275,280)
(276,279)(277,278);;
s2 := ( 1,149)( 2,148)( 3,154)( 4,153)( 5,152)( 6,151)( 7,150)( 8,156)
( 9,155)( 10,161)( 11,160)( 12,159)( 13,158)( 14,157)( 15,163)( 16,162)
( 17,168)( 18,167)( 19,166)( 20,165)( 21,164)( 22,170)( 23,169)( 24,175)
( 25,174)( 26,173)( 27,172)( 28,171)( 29,177)( 30,176)( 31,182)( 32,181)
( 33,180)( 34,179)( 35,178)( 36,184)( 37,183)( 38,189)( 39,188)( 40,187)
( 41,186)( 42,185)( 43,191)( 44,190)( 45,196)( 46,195)( 47,194)( 48,193)
( 49,192)( 50,198)( 51,197)( 52,203)( 53,202)( 54,201)( 55,200)( 56,199)
( 57,205)( 58,204)( 59,210)( 60,209)( 61,208)( 62,207)( 63,206)( 64,212)
( 65,211)( 66,217)( 67,216)( 68,215)( 69,214)( 70,213)( 71,219)( 72,218)
( 73,224)( 74,223)( 75,222)( 76,221)( 77,220)( 78,226)( 79,225)( 80,231)
( 81,230)( 82,229)( 83,228)( 84,227)( 85,233)( 86,232)( 87,238)( 88,237)
( 89,236)( 90,235)( 91,234)( 92,240)( 93,239)( 94,245)( 95,244)( 96,243)
( 97,242)( 98,241)( 99,247)(100,246)(101,252)(102,251)(103,250)(104,249)
(105,248)(106,254)(107,253)(108,259)(109,258)(110,257)(111,256)(112,255)
(113,261)(114,260)(115,266)(116,265)(117,264)(118,263)(119,262)(120,268)
(121,267)(122,273)(123,272)(124,271)(125,270)(126,269)(127,275)(128,274)
(129,280)(130,279)(131,278)(132,277)(133,276)(134,282)(135,281)(136,287)
(137,286)(138,285)(139,284)(140,283)(141,289)(142,288)(143,294)(144,293)
(145,292)(146,291)(147,290);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(294)!( 8, 43)( 9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)
( 15, 36)( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)
( 23, 30)( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 50, 99)( 51,100)
( 52,101)( 53,102)( 54,103)( 55,104)( 56,105)( 57,141)( 58,142)( 59,143)
( 60,144)( 61,145)( 62,146)( 63,147)( 64,134)( 65,135)( 66,136)( 67,137)
( 68,138)( 69,139)( 70,140)( 71,127)( 72,128)( 73,129)( 74,130)( 75,131)
( 76,132)( 77,133)( 78,120)( 79,121)( 80,122)( 81,123)( 82,124)( 83,125)
( 84,126)( 85,113)( 86,114)( 87,115)( 88,116)( 89,117)( 90,118)( 91,119)
( 92,106)( 93,107)( 94,108)( 95,109)( 96,110)( 97,111)( 98,112)(155,190)
(156,191)(157,192)(158,193)(159,194)(160,195)(161,196)(162,183)(163,184)
(164,185)(165,186)(166,187)(167,188)(168,189)(169,176)(170,177)(171,178)
(172,179)(173,180)(174,181)(175,182)(197,246)(198,247)(199,248)(200,249)
(201,250)(202,251)(203,252)(204,288)(205,289)(206,290)(207,291)(208,292)
(209,293)(210,294)(211,281)(212,282)(213,283)(214,284)(215,285)(216,286)
(217,287)(218,274)(219,275)(220,276)(221,277)(222,278)(223,279)(224,280)
(225,267)(226,268)(227,269)(228,270)(229,271)(230,272)(231,273)(232,260)
(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)(239,253)(240,254)
(241,255)(242,256)(243,257)(244,258)(245,259);
s1 := Sym(294)!( 1, 57)( 2, 63)( 3, 62)( 4, 61)( 5, 60)( 6, 59)( 7, 58)
( 8, 50)( 9, 56)( 10, 55)( 11, 54)( 12, 53)( 13, 52)( 14, 51)( 15, 92)
( 16, 98)( 17, 97)( 18, 96)( 19, 95)( 20, 94)( 21, 93)( 22, 85)( 23, 91)
( 24, 90)( 25, 89)( 26, 88)( 27, 87)( 28, 86)( 29, 78)( 30, 84)( 31, 83)
( 32, 82)( 33, 81)( 34, 80)( 35, 79)( 36, 71)( 37, 77)( 38, 76)( 39, 75)
( 40, 74)( 41, 73)( 42, 72)( 43, 64)( 44, 70)( 45, 69)( 46, 68)( 47, 67)
( 48, 66)( 49, 65)( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)
(105,107)(113,141)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)
(120,134)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(128,133)
(129,132)(130,131)(148,204)(149,210)(150,209)(151,208)(152,207)(153,206)
(154,205)(155,197)(156,203)(157,202)(158,201)(159,200)(160,199)(161,198)
(162,239)(163,245)(164,244)(165,243)(166,242)(167,241)(168,240)(169,232)
(170,238)(171,237)(172,236)(173,235)(174,234)(175,233)(176,225)(177,231)
(178,230)(179,229)(180,228)(181,227)(182,226)(183,218)(184,224)(185,223)
(186,222)(187,221)(188,220)(189,219)(190,211)(191,217)(192,216)(193,215)
(194,214)(195,213)(196,212)(246,253)(247,259)(248,258)(249,257)(250,256)
(251,255)(252,254)(260,288)(261,294)(262,293)(263,292)(264,291)(265,290)
(266,289)(267,281)(268,287)(269,286)(270,285)(271,284)(272,283)(273,282)
(275,280)(276,279)(277,278);
s2 := Sym(294)!( 1,149)( 2,148)( 3,154)( 4,153)( 5,152)( 6,151)( 7,150)
( 8,156)( 9,155)( 10,161)( 11,160)( 12,159)( 13,158)( 14,157)( 15,163)
( 16,162)( 17,168)( 18,167)( 19,166)( 20,165)( 21,164)( 22,170)( 23,169)
( 24,175)( 25,174)( 26,173)( 27,172)( 28,171)( 29,177)( 30,176)( 31,182)
( 32,181)( 33,180)( 34,179)( 35,178)( 36,184)( 37,183)( 38,189)( 39,188)
( 40,187)( 41,186)( 42,185)( 43,191)( 44,190)( 45,196)( 46,195)( 47,194)
( 48,193)( 49,192)( 50,198)( 51,197)( 52,203)( 53,202)( 54,201)( 55,200)
( 56,199)( 57,205)( 58,204)( 59,210)( 60,209)( 61,208)( 62,207)( 63,206)
( 64,212)( 65,211)( 66,217)( 67,216)( 68,215)( 69,214)( 70,213)( 71,219)
( 72,218)( 73,224)( 74,223)( 75,222)( 76,221)( 77,220)( 78,226)( 79,225)
( 80,231)( 81,230)( 82,229)( 83,228)( 84,227)( 85,233)( 86,232)( 87,238)
( 88,237)( 89,236)( 90,235)( 91,234)( 92,240)( 93,239)( 94,245)( 95,244)
( 96,243)( 97,242)( 98,241)( 99,247)(100,246)(101,252)(102,251)(103,250)
(104,249)(105,248)(106,254)(107,253)(108,259)(109,258)(110,257)(111,256)
(112,255)(113,261)(114,260)(115,266)(116,265)(117,264)(118,263)(119,262)
(120,268)(121,267)(122,273)(123,272)(124,271)(125,270)(126,269)(127,275)
(128,274)(129,280)(130,279)(131,278)(132,277)(133,276)(134,282)(135,281)
(136,287)(137,286)(138,285)(139,284)(140,283)(141,289)(142,288)(143,294)
(144,293)(145,292)(146,291)(147,290);
poly := sub<Sym(294)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope